No it doesn't have to be renewed before its validity expires.
The Directive currently governing EU driving licences is DIRECTIVE 2006/126/EC
. The Directive came into force in 2006. Member states had until 19 January 2011 to transpose its requirements into national law and until 19 January 2013 to apply the provisions. It replaced a number of previous directives.
I think the interpretation described earlier in the thread may be wrong. The UK is governed by the same Directive and, as described in this Ask the Police question
you can drive in the UK on a licence issued by another member state as long as the licence is valid. I don't see why the Greek police are not following this.
The problem really occurs when you need to renew the licence. You are supposed to obtain a licence from the member state where you are permanently resident. Each member state can only issue licences to individuals who live permanently in that member state. When you apply for a licence you are supposed to state your permanent address, not the address of a friend or relative. As far as I can see anybody who continues to drive in Greece on a valid UK licence for an extended period, even if they are permanently resident are not breaking any law. Anybody who renews a UK licence using a false UK address when they are permanently resident in Greece are breaking the law.